A man is playing tennis and a tennis ball (m=1.2 kg) approaches his tennis racket with a speed of 8.0 m/s. His racket is in contact with the ball for 2.0 ms and sends the ball flying in the opposite direction with a speed of 6.0 m/s. What is the magnitude of the average force he exerted on the ball using his tennis racket?
ECU up here all day!!!! lmao
To find the magnitude of the average force exerted on the ball, we can use Newton's second law of motion, which states that the force applied to an object is equal to the object's mass multiplied by its acceleration.
First, we need to find the acceleration of the ball during the contact with the racket. We can use the equation of motion:
v = u + at
Where:
v = final velocity of the ball after contact (6.0 m/s)
u = initial velocity of the ball before contact (-8.0 m/s)
t = time of contact (2.0 ms = 0.002 s)
Rearranging the equation, we have:
a = (v - u) / t
Substituting the given values:
a = (6.0 m/s - (-8.0 m/s)) / 0.002 s
Simplifying,
a = (6.0 m/s + 8.0 m/s) / 0.002 s
a = 14.0 m/s / 0.002 s
a = 7,000 m/s²
Now that we have the acceleration, we can use Newton's second law to calculate the force:
F = m * a
Substituting the given mass of the ball (m = 1.2 kg) and the calculated acceleration (a = 7,000 m/s²):
F = 1.2 kg * 7,000 m/s²
F = 8,400 N
Therefore, the magnitude of the average force exerted on the ball by the tennis racket is 8,400 N.